A213770 Antidiagonal sums of the convolution array A213768.

1, 7, 23, 58, 126, 250, 467, 837, 1457, 2484, 4172, 6932, 11429, 18739, 30603, 49838, 81002, 131470, 213175, 345425, 559461, 905832, 1466328, 2373288, 3840841, 6215455, 10057727, 16274722, 26334102, 42610594, 68946587, 111559197

Offset: 1

Author

Clark Kimberling, Jun 21 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

Crossrefs

Cf. A213768, A213500.

Programs

Magma

[2*Fibonacci(n+6)+Lucas(n+4)-n*(2*n+11)-23: n in [1..35]]; // Vincenzo Librandi, Jul 09 2019

Mathematica

(See A213768.)

Formula

a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).

G.f.: f(x)/g(x), where f(x) = x*(1 + 3*x) and g(x) = (1 - x - x^2)(1 - x)^3.

a(n) = 2*Fibonacci(n+6) + Lucas(n+4) - n*(2*n + 11) - 23. - Ehren Metcalfe, Jul 08 2019